This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Sunday, August 31, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q48

Mr Lim spent \$1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio of 3 : 2. A dictionary cost \$4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary.

Solution

(Note: The working has been amended (in blue) on 17 Sep 08 to make the working clearer.)

Cost of 1 dictionary ----- 1 unit + \$4
Cost of 1 comic ----- 1 unit

Comics ----- 120%
Dictionary ----- 100%
Total 220% ----- \$1496

10% ----- \$1496 divided by 22 = \$68
(Dictionaries) 100% ----- \$680

Comics ----- \$1496 - \$680 = \$816
But we know that the ratio
comics : dictionaries
3 : 2

Comics
3 units ----- \$816
1 unit ----- \$272

Dictionaries
2 units + ? groups of \$4 ------ \$680
(2 x \$272) + ? grps of \$4 ----- \$680
? grps of \$4 ----- \$680 - \$544 = \$136
? grps ----- \$136 divided by 4 = 34 groups of \$4

[Every \$4 difference ---- 1 dictionary was bought
\$136 difference ----- \$136 divided by \$4 = 34 (dictionaries)]

Dictionaries ----- \$680
\$680 divided by 34 dictionaries = \$20 per dictionary

## Friday, August 29, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q47

Najip, Kumar and Gurmit started jogging at the same time from the same starting-point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout.
a) What was the ratio of Gurmit’s speed to Najip’s speed to Kumar’s speed?

b) When Gurmit and Najip met again at the starting-point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track?

b)
(Gurmit)
5 min ----- 1 round
15 min ----- 3 rounds

Kumar (since ratio Gurmit : Kumar is 2:3) ----- 4.5 rounds
3.6 km divided by 4.5 rounds = 0.8 km per round

Answer: The circumference is 0.8 km

======

Update - 1420 hours, 29 Aug 2008

I have relabelled the model to make it clearer.
The model is seen from Gurmit’s perspective.
He was running in the opposite direction as compared to the other two.

In the 5 min cycle, Gurmit will see Kumar after 2 min.
This means G would have covered 2/5 of lap when he met K.
It also means K would have covered 3/5 lap at that point.
Hence, the model shows 2 units for G and 3 for K.

In the same 5 min cycle, G will meet N after 3 min.
This means G would have covered 3/5 lap when he met N.
Of course, N would have covered 2/5 lap.
Hence, 3 units for G and 2 for N.

## Thursday, August 28, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q46

A rectangular tank measuring 60 cm by 40 cm and 20 cm was 1/6 filled with water. At 08 00, Tap A with water flowing out at a rate of 3 litres per minute was turned on. At 08 02, Tap B was turned on to drain water out of the container at a fixed rate. At 08 13, the tank was 75% filled with water. At what time would the tank be filled to the brim?

Solution

Capacity of tank -----
(60 cm x 40 cm x 20 cm) = 48 000 cubic cm or 48 000 ml

1/6 of volume ----- 48 000 ml x 1/6 = 8000 ml

Water flowed for 2 min ----- 3 litres x 2 = 6000 ml

Amount of water in tank at 08 02 -----
8000 ml + 6000 ml = 14000 ml

75% volume ----- 48 000 ml x 75% = 36 000 ml

From 08 02 to 08 13 ----- 11 min

Rate of increase of water level in tank -----
(36 000 – 14 000) ml divided by 11 min
= 2000 ml per min

To be filled to the brim from 75% volume, another 25% volume must be filled.

25% volume ---- 48 000 ml x 25% = 1200 ml
Time needed ----- 12 000 ml divided by 2000 ml per min = 6 min

6 min after 08 13 is 08 19

Answer: It would be 08 19 when the tank is filled to the brim.

## Wednesday, August 27, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q45

400 people took part in a camp. 73 of them were adults and the rest were children. 2/5 of the boys and ¼ of the girls were lower primary pupils while the rest of them were upper primary pupils. There were 9 more upper primary girls than upper primary boys.
a) How many upper primary pupils were there?
b) What percentage of the people who took part in the camp were girls?

Solution

400 people – 73 adults ----- 327 children

12 parts + 15 parts ----- 981 + 45
27 parts ----- 1026
1 part ----- 1026 divided by 27 = 38

a)
(Upp Pri Girls) 3 parts ---- 3 x 38 = 114
(Upp Pri Boys) 114 – 9 = 105
Total Upper Pri ----- 114 + 105 = 219
Answer: There were 219 upper primary pupils.

b)
(Total Girls) 4 parts ----- 38 x 4 = 152
Percentage of girls ----- (152/400) x 100% = 38%

## Tuesday, August 26, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q44

The figure below is made up of a rectangle, a semi-circle and 4 identical quadrants.
a) What is the total area of the shaded parts?
b) What is the perimeter of the whole figure?

Solution

a) Redrawing

= Area of rectangle + Area of quadrant
= (7 cm x 3.5 cm) + (¼ x 22/7 x 3.5 cm 3.5 cm)
= (24.5 + 9.625) square cm

b)
Perimeter -----
Lengths of 4 quarter arcs + 6r
= 4 x (¼ x 2 x 22/7 x 3.5 cm) + (6 x 3.5) cm
= 22 cm + 21 cm

## Sunday, August 24, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q43

Taufik arranged a rectangle and a square and painted them in three colours as shown in the figure below. The ratio of the area of the rectangle to that of the square is 3:1. The ratio of the area of the red part to that of the blue part is 4:1. The length of the square is 9 cm.
a) What is the area of the purple part?

b) What is the ratio of the area of the purple part to that of the figure?

Area of Rectangle : Area of Square
3 : 1
9 units : 3 units

Red Area : Blue Area
4 : 1
8 units : 2 units

a)
(Square) 3 units ----- 81 square cm
(Purple) 1 unit ----- 81 square cm divided by 3 = 27 square cm (Answer)

b)
Purple ----- 1 unit
Whole figure 11 units

Area of purple part : Area of whole figure

## Thursday, August 21, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q42

The figure below shows a park which is made up of a triangular fitness area, a rectangular pond and a field in the shape of a trapezium. The length of the pond is twice its breadth.

a) The cost of fencing material is \$3 per meter. How much will it cost to fence up the pond?
b) What is the area of the park?

Solution

a)
Length of pond ----- 2 x 4 m = 8 m
Perimeter of pond ----- 2 x (8 + 4) m = 24 m

1 m ----- \$3
24 m ----- \$3 x 24 = \$72

Answer: It will cost \$72 to fence up the pond.

b)
Area of rectangle -----
21 m x 4 m = 84 square m

Area of triangle -----
½ x 14 m x 21 m = 147 square m

Total area of the park ----- (84 + 147) square m = 231 square meters (Answer)

## Wednesday, August 20, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q41

The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers was 1 : 5. Then their mother gave Eunice 12 more stickers and Andrew 5 more stickers. The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers became 1 : 4. How many stickers did Andrew have in the end?

Solution

Andrew (before) 1 unit + 5 ----- 1 part (after) (multiply by 4)
Eunice (before) 5 units +12 ----- 4 parts (after)

Andrew (before) 4 units + 20 ----- 4 parts (after)
Eunice (before) 5 units + 12 ----- 4 parts (after)

Comparing Eunice with Andrew -----
(Eunice) 5 units + 12 ----- 4 units + 20 (Andrew)

5 units – 4 units ----- 20 – 12
1 unit = 8

Andrew in the end -----
1 unit + 5
= 8 + 5
= 13

## Tuesday, August 19, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q40

Kavita had 50% fewer erasers than Mark. After Mark gave 15 of his erasers to Kavita, Kavita had 40% fewer erasers than Mark. How many erasers did Kavita have at first?

Solution

Kativa has 30 more, while Mark has 15 less. Hence, Kativa will have 45 more than Mark.

45 ----- 120% - 100%
45 ----- 20%
10% ----- 45% divided by 2 = 22.5%

Kativa at first ----- 60% -15
= (6 x 22.5) - 15
= 135 – 15
= 120

## Sunday, August 17, 2008

### Pei Chun Public Sch 2007 PSLE Math Prelim Q38

A rectangular piece of cardboard measures 17 cm by 12 cm. Sushila cuts the greatest number of rectangular pieces, each measuring 3 cm by 2 cm, from the cardboard. What is the total area of all the pieces cut?

Solution
The diagram below is not drawn to scale

34 pieces of small rectangles can be cut without any cardboard left.

Area used ----- 17 cm x 12 cm = 204 square cm (Answer)

### Pei Chun Public Sch 2007 PSLE Math Prelim Q39

A group of pupils were asked to choose a co-curricular activity. The pie chart represents their choices. The same number of pupils chose Basketball and Volleyball.
a) 60 pupils chose Table Tennis. How many pupils chose Basketball?
b) The ratio of the number of pupils who chose Basketball to the number of pupils who chose Soccer is 3 : 10. How many pupils chose Scouts?

Solution

a)
Table Tennis (1/4 pie chart) ----- 60
Basketball (1/2 x Table Tennis) ----- ½ x 60 = 30

b)
Soccer + Scouts (1/2 pie chart) ----- 60 x 2 = 120

3 : 10
30 : 100

If 100 chose soccer, Scouts ----- 120 – 100 = 20

## Wednesday, August 13, 2008

PSLE English Oral is just a day away. Here is a link to Paya Lebar MGS's video on English Oral Exam.

### Pei Chun Public Sch 2007 PSLE Math Prelim Q37

Mrs Durai wants to buy bookmarks for 3 classes of pupils. There are 35 pupils in each class. For every 4 bookmarks she buys, she gets another one free.
a) How many bookmarks does she need if each pupil gets 1 bookmark?
b) 4 bookmarks cost \$2. What is the least amount she needs to pay?

Solution

a)
3 classes x 35 = 105

b)
4 bookmarks + 1 free ----- \$2
5 bookmarks (total) ----- \$2

105 bookmarks divided by 5 ----- 21 (groups of 5 bookmarks)

21 groups of 5 bookmarks ----- 21 x \$2 = \$42

Answer: She has to pay \$42.

## Monday, August 11, 2008

Fittingly, just before the exams, the Straits Times publishes an article about the atrocious state of handwriting of some students. (The full article can be found at the end of this post.)

For whatever reason, some students never learn. Even after much advice from teachers and nagging from parents, some students simply would not write legibly. They believe that the world is able to read their handwriting, and even will argue with markers that they deserve the marks, after the exam is over.

The rule is simple. If the marker cannot make out what you write, he/she will not be able to give you the marks.

The importance of handwriting cannot be under-emphasized. For example for Science, key words must be spelt correctly. It is useless arguing with markers after the exam that what you wrote is “stomata”, when what it looks like to everybody else, as “stomota”.

The student may argue all he wants that the marker mis-read his writing. From the marker’s viewpoint, the student did not know the correct spelling of the keyword. If the marker awards the student the mark, it would be unfair to students who genuinely got the answer right.

For the PSLE, although there is an avenue for appeal, students will NEVER get to see their papers after the exam. What this means is that if the markers cannot read your handwriting, and if you lose marks for that, you will have no one to blame but yourself.

The saddest part is that you will never know if you lost marks because you got the answers wrong, or because no one understood what you wrote.

From the Straits Times

Wired teens = 'Ant' writing
Students don't see need to improve handwriting because of tech tools but teachers hate it

BLAME technology for 'ants' - or what teachers call bad teen handwriting.

The Straits Times collected samples from 186 teens aged 13 to 17, which threw up 52 scripts covered with 'ants'.

They needed a lot of deciphering, typical of handwriting of the wired generation, said handwriting expert William Pang, 60.

Mr Pang, a handwriting consultant who began studying the science of handwriting analysis in the 1970s, blames this 'degeneration' on the lack of focus on penmanship in classrooms.

Students are not taught to grasp the pen properly, he said. 'Some of them even slump on the table as they write.'

They do not see the need to improve, either. After all, 'technology helps to make homework neater for students', Mr Pang pointed out.

Modern practices like downloading notes from the school's website and submitting typewritten assignments lessen the need for legible handwriting.

Teachers, who have to wade through an average of 100 to 200 scripts each week, say they especially hate the type of handwriting they call 'ants'.

'The tiny, ant-size writing makes it difficult for teachers to read what is written,' lamented Mrs Kang Yeok Lung, 59, a senior teacher at St Andrew's Junior College.

She has been a teacher for 27 years, and points out: 'When students write like that, they don't realise that the teacher's eyesight is affected and it makes marking a chore.'

The cure?

'I think assignments should be handwritten and not sent to the teacher as an e-mail attachment,' Mrs Kang said.

After all, when teachers have to guess what students write, she added, 'the student loses out'.

Especially during examinations, when essays are still handwritten, it can cost them grades. When markers cannot understand the scripts, 'there is a higher risk of misinterpretation'.

Augustus Set, 17, a second-year student at St Andrew's Junior College, said his parents feared his bad writing so much, they bought him handwriting practice books, 'so that I can write more legibly for my A level examinations'.

Still, other students are recalcitrant - they say they are expressing themselves.

Said Sayyed Amir Zaini, 16, a Secondary 4 student at Pasir Ris Secondary School: 'I tried to change my handwriting but I just can't. Anyway, I don't think I should change it just because others say so. I will change my handwriting only because I want to.'

Handwriting in the 1970s was of a better quality, said Mr Pang, who was then studying close to 300 handwriting samples as an amateur analyst. Tidier scripts showed that Singaporeans were more patient and considerate then.

'People were in less of a rush,' he said. 'They took more pains with their handwriting and the letters were more well-formed... to ensure others could read what they had written.'

The Straits Times' survey, on the other hand, revealed that many of the wired generation are disconnected, individualistic, more rebellious and non-conformist than their predecessors.

Mr Pang believes that teens will change their handwriting as they grow older 'to create their own identity'.

But that might not be for the better, he warned: 'A person's handwriting is likely to get worse with age if at work, he types more than he writes.'

### Maha Bodhi Sch 2007 PSLE Math Prelim Q48

Two different machines, A and B, were used together at the same time to print a book. It took two hours for the book to be printed. If only Machine A was used, it would have taken another 4 hours. How long would it take to print the same book if only Machine B was used?

Solution

Machine A only ----- 2 hours + 4 hours = 6 hours

6 hours ----- Machine A printed whole book
2 hours ----- Machine A printed 1/3 book

The other 2/3 of the book was printed by Machine B
2 hours ----- Machine B printed 2/3 book
2/3 book ----- 2 hours
3/3 book ----- 3 hours

Answer: It would take 3 hours if Machine B was used only.

## Friday, August 08, 2008

### Maha Bodhi Sch 2007 PSLE Math Prelim Q47

Ali, Bala and Krishnan went to a shopping centre and bought a present for their friend. They agreed to share the cost of the present equally but Ali did not have any money with him that day and Bala did not bring enough to pay for his share. As a result, the amount of money Bala paid to that paid by Krishnan was 1 : 4. The next day, Bala returned \$12 to Krishnan.

Find
a) how much money Bala brought along with him to the shopping centre.
b) the cost of the present.

Solution

Bala : Krishnan
1 : 4

1 + 4 = 5
5 units to be shared by 3 people -----
5 units divided by 3 = 1 and 2/3 units

Each person was expected to pay 1 and 2/3 units.

a)
Bala paid 1 unit the previous day, but paid \$12 the next day, hence,

The balance 2/3 unit ----- \$12
1/3 unit ----- \$12 divided by 2 = \$6
1 unit ----- \$6 x 3 = \$18

b)
Total cost ----- 5 units
5 units ----- \$18 x 5 = \$90

Answer: The cost of the present was \$90.

## Thursday, August 07, 2008

### Maha Bodhi Sch 2007 PSLE Math Prelim Q46

Each corner of the floor mat shown above is made up of a quadrant of radius 4 cm. Find the perimeter of the floor mat.

Solution
4 quadrants make 1 full circle
Perimeter of arcs of 4 quadrants above -----
2 x 3.14 x 4 cm = 25.12 square cm

Consider length of mat -----
40 cm – 4 cm – 4 cm = 32 cm

30 cm – 4 cm – 4 cm = 22 cm

Perimeter of mat -----
(25.12 + 32 cm + 32 cm + 22 cm + 22 cm)

## Wednesday, August 06, 2008

### Maha Bodhi Sch 2007 PSLE Math Prelim Q45

In a frog-leaping competition, for every two leaps made by a big frog, a small frog would have to leap thrice. In a 100-m race, the big frog leapt 50 times.
a) How many times did the small frog leap?
b) How many metres did the small frog move with each leap?

Solution

a)
Big frog ----- small frog
2 leaps ----- 3 leaps
(x 25) 50 leaps ----- 75 leaps (x25)

Answer: The small frog leapt 75 times.

b)
100 m divided by 75 leaps ----- 1 and 1/3 m per leap (Answer)

## Tuesday, August 05, 2008

### Free Ai Tong P5 2006 CA2 Maths Section C Worked Solutions

A brand new free copy of Section C Maths worked solutions for P5 is now available.

To get your free copy (in PDF format) of the above, email us -

freemathsample@gmail.com

Send us a message “Free Ai Tong P5 Maths Solutions”.

Please allow a working day or two for us to reply you.

Below are sample screenshots of the free copy. You may click on the images to enlarge them.

### Ai Tong School P5 CA2 2006 Math Q37

The average length of 2 ribbons is 2 m. One ribbon is 50 cm longer than the other. Find the ratio of the length of the shorter ribbon to that of the longer ribbon.

Solution

Shorter ----- 1 unit
Longer ----- 1 unit + 50 cm
Total Length ----- 2 units + 50 cm

Average length of 2 ribbons ----- 2 m or 200 cm
Total length of 2 ribbons ----- 200 cm x 2 = 400 cm

(Total) 2 units + 50 cm ----- 400 cm
2 units ----- 400 cm – 50 cm = 350 cm
1 unit ----- 350 cm divided by 2 = 175 cm

Shorter ribbon ----- 175 cm
Longer ribbon ----- 175 cm + 50 cm = 225 cm

Ratio
Shorter : Longer
175 : 225
7 : 9

Answer: The ratio of the shorter ribbon to that of the longer ribbon is 7:9.

### Ai Tong School P5 CA2 2006 Math Q36

Solution

(After)
Agnes ----- 1 unit
Mabel ----- 5 units
Total 6 units ----- 720

1 unit ----- 720 divided by 6 = 120

Mabel at first
5 units – 72 ----- (120 x 5) – 72 = 528

## Monday, August 04, 2008

### Maha Bodhi Sch 2007 PSLE Math Prelim Q44

Two motorists, X and Y, travelled on the same route from Town A to Town B. They each drove at a uniform speed but started their journey at a different time of the day.

The table below shows some details of their journey.

If Motorist X reached Town B at 1625, find:
a) the distance between the two towns and
b) the speed at which Motorist Y was travelling.

Solution

a)
Consider Motorist X -----
Distance (middle portion) ----- 120 km/h x 2.5 h = 300 km
Total Distance covered ---- 60 km + 300 km + 60 km = 420 km

Answer: The total distance was 420 km.

b)
Motorist Y -----
Middle portion ----- 420 km – 100 km – 100 km = 220 km
Speed ----- 220 km divided by 2.5 hours = 88 km/h

Answer: Speed of Motorist Y was 88 km/h.

## Saturday, August 02, 2008

### Glitch fixed

A particular visitor-counting widget was giving problems around midnight of 1 Aug 2008 to 0800 hours on 2 Aug 2008, blocking visitors from this site.

The widget has since been removed and we are back up.

Apologies for the inconvience caused.

Regards
Excel Eduservice

Update 3 Aug 2008, 0810 hr - the abovementioned widget has been fixed. Widget has been reinstalled.

## Friday, August 01, 2008

### Maha Bodhi Sch 2007 PSLE Math Prelim Q43

Using 3/5 of his money, Derek could buy 8 similar pens. If he was given an extra dollar, he could use it together with the rest of his money to buy another 6 such pens. How much money had Derek?

Solution

3 units ----- 8 pens (multiply by 2)
2 units + \$1 ----- 6 pens (multiply by 3)

6 units ----- 16 pens
6 units + \$3 ----- 18 pens

\$3 ----- 18 pens – 16 pens = 2 pens
2 pens ----- \$3
1 pen ----- \$3 divided by 2 = \$1.50

14 pens ----- \$1.50 x 14 = \$21
Less \$1 he was given ----- \$21 - \$1 = \$20